Method and apparatus for correcting excess signals in an imaging system

ABSTRACT

A method and apparatus for excess signal compensation in an imaging system is described. In one particular embodiment, the invention provides for non-linear background, offset (due to time dependent dark current) and/or lag (including constant, linear and non-linear terms, due to image persistence) corrections of large area, flat panel imaging sensors.

RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No. 12/619,624 filed Nov. 16, 2009 issued as U.S. Pat. No. 8,049,156 on Nov. 1, 2011, which is a divisional of U.S. patent application Ser. No. 12/205,768 filed Sep. 5, 2008 issued as U.S. Pat. No. 7,638,752 on Dec. 29, 2009, which is a continuation of U.S. patent application Ser. No. 11/729,611 filed Mar. 29, 2007 issued as U.S. Pat. No. 7,423,253 on Sep. 9, 2008, which is a continuation of U.S. patent application Ser. No. 10/688,484 filed Oct. 16, 2003 issued as U.S. Pat. No. 7,208,717 on Apr. 24, 2007 which claims the benefit of U.S. Provisional Patent Application No. 60/419,132, filed Oct. 16, 2002.

TECHNICAL FIELD

This invention relates generally to large area, flat panel imagers. More specifically, the invention relates to amorphous silicon and/or organic semiconductor thin-film-transistor (TFT) or diode-switched array imagers.

BACKGROUND

Large area flat panel imagers function by accumulating charge on capacitors generated by pixels of p-i-n photodiodes (amorphous silicon or organic semiconductor) with scintillators or by pixels of photoconductors. Typically, many pixels are arranged over a surface of the imager where TFTs (or single and/or double diodes) at each pixel connect the charged capacitor to a read out amplifier at the appropriate time. A pixel is composed of the scintillator/photodiode/capacitor/TFT or switching-diode combination or by the photoconductor/capacitor/TFT or switching-diode combination. Often the photodiode intrinsically has enough capacitance that no separate charge storage capacitor is required. As illustrated in FIG. 1A, radiation (e.g., alpha, beta, gamma, X-ray, neutrons, protons, heavy ions, etc.) strikes the scintillator and causes the scintillator to generate visible light. The visible light strikes a photodiode and generates an electric current. Alternatively, an imager may be configured such that the radiation strikes a biased photoconductor to generate the electric current, as illustrated in FIG. 1B. The current charges a capacitor (where the illustrated capacitor includes the self capacitance of the photoconductor) and leaves a charge on the capacitor. The integrated charge on the capacitor is proportional to the integrated light intensity striking the respective photoconductor for a given integration time. At an appropriate time, a switch (e.g., a TFT or switching diode(s)) activates and reads out the charge from the capacitor onto a charge sensitive amplifier (not shown).

For long integration times, typically over 20 seconds for amorphous silicon technology, there is a linear increase in charge Q_(Li) to the capacitor charge (in coulombs) of pixel “i,” as a function of discrete frame time T, due to a constant leakage (or dark) current from the switch (e.g., TFT), diode or photodetector. This dark current I_(D) is on the order of 1-2 femtoamps (fA) for 100 to 200 micron wide pixels of amorphous silicon TFT construction. The expression for Q_(Li) is the dark current I_(D) multiplied by T. Dark current I_(D) may be constant or time varying; giving an excess charge Q_(E) contribution that is either linear or non-linear with respect to time, respectively. This linear dark charge contribution to Q_(Li) is subtracted from the total charge Q_(Ti) read off the capacitor of pixel “i” in order to provide the true image charge Q_(Si). Subtracting the dark-current charge contribution (either linear or non linear), from the total charge Q_(Ti) read off the capacitor, is called background (or offset) correction.

In addition to dark current charge contributions from the switch (e.g., TFT) there are leakage (or dark) current charge contributions from the capacitor and the photodiode. The true image charge Q_(Si) is obtained by subtracting the background (or offset) dark charge contributions from the measured charge Q_(Ti) of pixel “i.” The simplest background correction method is to subtract a constant fraction of the charge that was present on pixel “i” during at least one, and sometimes additional, prior frames.

Prior background correction methods have been implemented to estimate offset correction. One prior background correction method discussed in U.S. Pat. No. 5,452,338, isolates the offset image by acquiring an image when the detector is not exposed to X-rays, using the same timing used in acquiring the X-ray exposed images. The image acquired after exposure is then subtracted from future frames. One problem with the use of one single frame in determining the offset correction is the offset image introduces additional noise. To reduce the additional noise, multiple non-exposed images may be acquired and then averaged. One problem using a single image or an average of multiple images is the offset signals may drift with time, temperature, and other extrinsic factors while the single image or averaged image remains constant.

Another prior background correction method discussed in a paper by Sussan Pourjavid, et al., entitled “Compensation for Image Retention in an Amorphous Silicon Detector” (SPIE Conference on Physics of Medial Imaging, February 1999), and U.S. Pat. No. 5,452,338, continuously updates the offset images to compensate for drift in the offset signals. The method, described in the above references, models the time response of the background contribution from leakage current (or dark image) in the diodes as a linear time variant system (LTI) using linear systems theory (least square method). The LTI system derived from the response model is then used to predict the offset needed for image correction. However, in modern medical imaging equipment, for example, there is a demand for real-time, 30 frames per second images, where scans are made with 33 millisecond integration times. Even more advanced imaging applications, like computed tomography, can use even higher frames rates of 120, 360 or even 900 frames per second, corresponding to respective integration times of 8, 3 and 1 milliseconds, respectively. Background correction using least square prediction of discrete frame time in such situations is not as effective. With near real-time imaging, for example 3 frames per second (FPS) or faster, background correction with least square prediction can introduce significant image errors and artifacts. A more effective method for background (or offset) correction is needed in short-integration-time imaging applications.

SUMMARY OF AN EMBODIMENT OF THE INVENTION

The present invention pertains to a method and apparatus for excess charge corrections in flat panel imaging sensors.

Additional features and advantages of the present invention will be apparent from the accompanying drawings, and from the detailed description that follows below.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example and not intended to be limited by the figures of the accompanying drawings.

FIG. 1A is an illustration of conventional components of an imager sensor array.

FIG. 1B illustrates an alternative configuration of an imager sensor array.

FIG. 2A illustrates one embodiment of an imaging system.

FIG. 2B illustrates one embodiment of an imager sensor array.

FIG. 2C illustrates another embodiment of an imager sensor array.

FIG. 3 illustrates one example of a graph of excess current generated by both a constant and time varying excess current components.

FIG. 4 is one expression for a time varying excess current I_(E) and its integration with time to determine an excess charge Q_(E) that is non-linear in time.

FIG. 5 illustrates one example of a graph showing time varying excess or leakage current for multiple TFTs connected in parallel.

FIG. 6 illustrates a table correlating frame rate with integration time.

FIG. 7 is a flow diagram illustrating one embodiment of a method of estimating the excess signal and compensating for the excess signal in an imaging system.

FIG. 8 is a flow diagram illustrating one embodiment of a method of estimating the excess signal using one reference image frame, and compensating for the excess signal in an imaging system.

FIG. 9 is a flow diagram illustrating one embodiment of a method of estimating the excess signal using two reference image frames, and compensating for the excess signal in an imaging system.

FIG. 10A illustrates an exemplary fluoroscopic image frame after radiographic exposure without compensation for the excess signal.

FIG. 10B illustrates an exemplary fluoroscopic image frame after radiographic exposure with compensation for the excess signal.

FIG. 11A illustrates an exemplary fluoroscopic image frame of a pelvis phantom after radiographic exposure without compensation for the excess signal.

FIG. 11B illustrates an exemplary fluoroscopic image frame of a pelvis phantom after radiographic exposure with compensation for the excess signal.

FIG. 12 illustrates one example of a graph showing measured signal levels in an imaging system as a function of time.

FIG. 13 illustrates another example of a graph showing measured signal levels in an imaging system as a function of time.

FIG. 14 illustrates another example of a graph showing the measured signal levels in an imaging system as a function of time.

FIG. 15 illustrates one example of a look-up table.

FIG. 16A illustrates one example of a graph showing the remaining excess signal after compensation using different estimation methods.

FIG. 16B illustrates one example of a graph showing the remaining excess signal after compensation of two estimation methods at a smaller scale than FIG. 16A.

DETAILED DESCRIPTION

In the following description, numerous specific details such as specific materials, processing parameters, processing steps, etc., are set forth in order to provide a thorough understanding of the invention. One skilled in the art will recognize that these details need not be specifically adhered to in order to practice the claimed invention. In other instances, well known processing steps, materials, etc., are not set forth in order not to obscure the invention.

Some portions of the description that follow are presented in terms of algorithms and symbolic representations of operations on data bits that may be stored within a memory and operated on by a processor. These algorithmic descriptions and representations are the means used by those skilled in the art to effectively convey their work. An algorithm is generally conceived to be a self-consistent sequence of acts leading to a desired result. The acts are those requiring manipulation of quantities. Usually, though not necessarily, these quantities take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated. It has been proven convenient at times, principally for reasons of common usage, to refer to these signals as bits, values, elements, symbols, characters, terms, numbers, parameters, or the like. The term “coupled” as used herein means coupled directly to, or indirectly through one or more intervening components. References to charge may be expressed in terms of current integrated over time. Current is the amount of electric charge flowing past a specified circuit point per unit time.

The invention provides a method and apparatus for correction of image artifacts in imaging sensors due to excess charge. Sources of excess charge may be contributed by, for examples, leakage currents, offset (due to time dependent dark current), and lag currents (including constant, linear and non-linear terms, due to image persistence). The dark current charge contributions may be introduced from the switch (e.g., TFT). The leakage (or dark) charge contributions may be introduced from the capacitor and the photodiode. There may be persistent or “lag” charge contributions (and pixel capacitor charge contributions) from the photoconductor/photodiode or from incomplete charge read out from the capacitor, in a given frame of prior frames subjected to high dose radiation exposure. This “lag” charge contribution can be either linear or non linear in a discrete frame time T. Lag charge contributions are particularly prevalent when one frame is bright and the next is dark.

For purposes of the discussion hereafter, the term signal refers to the digital output of an imager, for example, as may be generated at the output of A/D converters 17 discussed below in relation to FIG. 2A. The digital signal (e.g., S_(E) 235) is generally proportional to the measured charged (e.g., Q_(E) 35) on the output of the imager sensor array 16, as is known in the art.

In one embodiment, the method includes determining an integration time based on the frame rate of the images and calculating a non-linear background signal S_(NLi) and/or prior-frames-dependent lag signal S_(LAGi) per pixel “i.” The lag signal S_(LAGi) may be a constant fraction of the true image signal S_(Si) of pixel “i,” or a constant fraction of the measured signal S_(Ti) of pixel “i,” from one or more prior frames with appropriate weighting factors. In order to correct images, the method may include subtracting the lag signal S_(LAGi) and the non-linear background signal S_(NLi) from the measured signal S_(Ti) representative of the charge on the capacitor of each pixel “i” for each image frame.

For faster than 0.1 frames per second, one method of generating the true image signal S_(Si) of pixel “i,” is to estimate the modeled (or theoretical or simulated), time-dependent, excess (e.g., leakage, dark, and lag) charge as a function of time from zero to an integration time. Another method of calculating true image signal S_(Si) is to integrate a smooth curve fit of experimental data of the time dependent excess charge as a function of time. One value for the integration time is the reciprocal of the frame rate. The estimated excess current is composed of the non-linear background signal S_(NLi) and/or of the calculated lag signal S_(LAGi) is subtracted from a measured signal S_(Ti) of a pixel “i” in order to produce the true image signal S_(Si) of pixel “i,” typically with frame rates faster than 0.1 frames per second.

In one embodiment, the method includes estimating the excess signal S_(E) (representative of the excess charge Q_(E)) by using a reference image frame when the end of exposure time of a high-dose radiographic image is known. The method determines the difference between the frame time of the reference image frame and the end of exposure time of the high-dose radiographic image. In one embodiment, the excess signal may be estimated using a power function. The power function uses the measured signal S_(T) (representative of a measured charge) of the reference image frame and the difference in time between the frame time of the reference image frame and the end of exposure time to determine a coefficient. The coefficient is then multiplied by a time-varying algebraic decay to estimate the excess signal S_(E). The excess signal S_(E) is the integral of the excess signal over the frame time. In another embodiment, the excess signal may be estimated using a look-up table. One example of using a look-up table may include indexing a pre-calculated excess signal S_(PRE) to estimate the excess signal S_(E) (representative of the excess charge Q_(E)) using a post exposure number of frames and measured signal S_(T) of the reference image frame. The difference in time is then converted to a frame number based on the frame rate. Once the excess signal S_(E) has been estimated using at least one of the power function and the look up table, the method may include subtracting the estimated excess signal S_(E) from the measured signal S_(T) for an image frame. Subtracting the estimated excess signal S_(E) of the image frame may remove significant image errors and artifacts that may appear in the present frame as “ghost images” from radiation incidents during one or more prior frames.

In another embodiment, the method includes estimating the excess signal S_(E) by using two reference image frames at two different frame times. Two reference image frames may be selected when the end of exposure time of a high-dose radiographic image is unknown. The two frame times of the two reference image frames may be based on the frame rate, and may be represented as frame numbers of the selected reference image frames. The method determines the difference in time between the two frame times and the frame time of the image selected for compensation. In one embodiment, estimating the excess signal S_(E) may be done using a power function. The power function uses the total measured signal S_(T) of at least one of the two reference image frames and the difference in time between the two reference image frames to determine a coefficient. The coefficient is then multiplied by a time-varying algebraic decay to estimate the excess signal S_(E). In another embodiment, the excess signal S_(E) may be estimated using a look-up table. One example of using a look-up table may include indexing a pre-calculated excess signal S_(PRE) to estimate the excess signal S_(E) using the frame number and measured signal S_(T) of at least one of the two reference image frames. It should be noted that, in this embodiment, the frame number s determined using the difference in time between the frame times of the two reference image frames. The difference in time is then converted to a frame number based on the frame rate. In another embodiment, the excess signal S_(L) may be estimated using a recursive function. One example of using a recursive function to estimate the excess signal S_(E) includes using the measured signal S_(T) of at least one of the two reference image frames selected and the difference in time between the two frame times of the two reference image frames to determine a previous frame coefficient. The previous frame coefficient is then used to determine a next frame coefficient. The next frame coefficient is then multiplied by the measured signal S_(T) of the reference image frame to estimate the excess signal S_(E) of the next frame. Once the estimation of excess signal S_(E), has been determined using either the power function, and/or the look up table, and/or the recursive function, the method may include subtracting the estimated excess signal S_(E) from the measured signal S_(T) of an image frame. Subtracting the total excess signal S_(E) on an image frame may remove significant image errors and artifacts that may appear in the present frame as “ghost images” from radiation incidents during one or more prior frames, such as frames of high-dose radiographic exposure.

FIG. 2A illustrates one embodiment of an imaging system. Imaging system 2 includes a computing device 4 coupled to an imager sensor array 16. Imager sensor array 16 may be, for example, an amorphous silicon organic semiconductor TFT or diode-switched array imager. As previously discussed in relation to FIGS. 1A and 1B, imager sensor array 16 functions by accumulating charge on capacitors generated by pixels of p-i-n photodiodes (amorphous silicon or organic semiconductor) with scintillators or by pixels of biased photoconductors. Typically, many pixels are arranged over a surface of imager sensor array 16 where, for example, TFTs (or single and/or double diodes) at each pixel connect a charged capacitor to charge sensitive amplifier 19 at the appropriate time. Charge sensitive amplifiers 19 drive analog to digital (A/D) converter 17 that, in turn, converts the analog signals received from amplifiers 19 into digital signals (e.g., S_(T), S_(E)) for processing by computing device 4. A/D converter 17 may be coupled to computing device 4 using, for example, I/O device 10 or interconnect 14. A/D converter 17 and charge sensitive amplifiers 19 may reside within computing device 4 or imager sensor array 16 or external to either device.

Computing device 4 implements the methods for correction of imaging sensors due to excess signal S_(E) representative of the excess charge Q_(E) discussed herein. The methods that may be performed by computing device 4 constitute computer programs made up of computer-executable instructions illustrated as steps in the following examples of the methods illustrated in the following figures. In one embodiment, computing device 4 includes a processor 6, storage device 8, input/output (IO) device 10, and memory 12 that are all coupled together with interconnect 14, such as a bus or other data path. In another embodiment, the computing device may be implemented using Programmable Logic Devices (PLD) or Field Programmable Gate Arrays (FPGA), in which the mathematical operations are performed by physical devices like adders, multipliers, etc. In another embodiment, the computing device may be implemented using specialized integrated circuits for data processing like adders, multipliers, bus switches, registers, RAM, ROM logic gates, etc.

Processor 6 represents a central processing unit of any type of architecture (e.g. Intel architecture or Sun Microsystems architecture), or hybrid architecture. In addition, processor 6 could be implemented in one or more semiconductor chips. Storage device 8 represents one or more mechanisms for storing data and/or instructions such as the method steps of the invention. Storage device 8 represents read-only memory (ROM), random access memory (RAM), magnetic disk storage media, optical storage media, flash memory devices, and/or other machine-readable media. Interconnect 14 represents one or more buses (e.g., accelerated graphics port bus, peripheral component interconnect bus, industry standard architecture bus, X-Bus, video electronics standards association related buses, etc.) and bridges (also termed bus controllers). I/O device 10 represents any of a set of conventional computer input and/or output devices including, for example, a keyboard, mouse, trackball or other pointing device, serial or parallel input device, display monitor, plasma screen, or similar conventional computer I/O devices. Memory 12 represents a high-speed memory device for retaining data and processor instructions for processor 6 according to the method steps of the invention. Memory 12 can be implemented using any of the memory devices described above for storage device 8. In addition, memory 12 can be used as a data cache for processor 6. While this embodiment is described in relation to a single processor computer system, in another embodiment, the invention may be implemented in a multi-processor computer system.

FIG. 2B illustrates one embodiment of the sensor array components of an imager. Imager sensor array 16 includes a bias voltage 27, a photoconductor 26, capacitor 28, and switch 32. Radiation 24 (X-rays, alpha, beta and gamma particles, neutrons etc.) has various energies depending on the particular embodiment of imager sensor array 16. In another embodiment the imager sensor array 16, illustrated in FIG. 2C, comprises a photodiode 26 a receives visible light 25 from a scintillator 26 b. The scintillator 26 b receives radiation 24 (e.g., alpha, beta, gamma, X-ray, neutron, proton, etc.) and generates visible light 25. Visible light 25 strikes photodiode 26 a and generates an electric current I 29.

In an alternative embodiment, imager sensor array 16 may have other configurations. For example, photoconductor 26 of FIG. 2B may be a phototransistor that directly receives radiation 24. In such an embodiment, the radiation 24 striking the biased phototransistor generates the electric current I 29.

The electric current I 29 charges capacitor 28 and leaves a charge value on capacitor 28, where the integrated charge on capacitor 28 is proportional to the integrated light intensity striking photoconductor 26 for a given integration time. Capacitor 28 is coupled to switch 32 (e.g., a TFT or switching diodes). At an appropriate time, the control input 30 (e.g., gate of a TFT) activates switch 32 and reads out the charge on capacitor 28 at node 34. The measured electric charge Q_(T) 36 at node 34 may include the excess charge Q_(E) 35.

One source of excess charge Q_(E) 35 is switch 32. The operation of switch 32 is discussed below in relation to a TFT for ease of discussion purposes only. In another embodiment other types of switching devices may be used, for example, switching diodes, and may also be sources of excess charge Q_(E) 35. When the charge value on capacitor 28 is read at node 34 there may be leakage current from gate 30 that contributes to the detected measured charge Q_(T) 36 at node 34. Other sources of excess charge Q_(E) 35 may be capacitor 28 and photoconductor 26. Lag from photoconductor 26 (or from photodiode 26 a) arises from charge remaining in the present frame generated by radiation incident during one or more prior frames, resulting in a “ghost image” of these earlier frames. In addition, lag arises from incomplete discharge of the capacitor 28 due to insufficiencies like too few RC time constants during readout to completely discharge capacitor 28. If the lag source is persistent photocurrent from the photoconductor 26, one method to compensate for lag charge in a current pixel may be to subtract a fraction of the true image signal S_(i) of one or more prior frames from the true image signal S_(i) of the current pixel. If the lag source is a result of incomplete readout discharge of the capacitor 28, one method to compensate for the excess charge 35, may be to subtract a fraction of the measured signal S_(Ti) from one or more prior frames. Image correction for the excess signal S_(E) (representative excess charge Q_(E) 35) composed of non-linear background signal S_(NLi) and/or lag signal S_(LAGi) may be increasingly helpful at imaging rates above 0.1 frames per second. Excess signal S_(E) may arise from other components that may be coupled to capacitor 28. Subtracting the excess signal S_(E) 235 from the measured charge S_(Ti) 236 provides the true image signal S_(Si) 239 of an image of FIG. 2A.

FIG. 3 illustrates one example of a graph from an amorphous silicon sensor showing measured capacitor charge (in femtocoulombs or fC), from excess current, estimated with a constant current component varying linearly with time, and estimated time varying current varying non-linearly with time. The horizontal axis of graph 300 shows time in seconds while the vertical axis shows capacitor charge in fC. Measured charge is the charge accumulated on the capacitor during the integration time (frame time), typically 30 milliseconds to 1000 milliseconds.

Measured charge 310 through the TFT of FIG. 1 is measured, in one example, by enabling the TFT (putting it in a low impedance state) for a short time (e.g., 5 to 200 microseconds) and transferring the charge accumulated on the sensor capacitor to a charge integration amplifier. Estimated constant measured charge with time, caused by the constant current 320, provides accurate estimation with image acquisition times greater than 20 seconds, as shown in graph 300. At image acquisition times below 20 seconds, the non-linear contribution Q_(Nli), caused by the non-linear current, has an increased effect on pixel charge correction.

One modeled expression for non-linear charge correction Q_(NLi) 330 is shown in FIG. 4. I_(E)(t) is one expression for current varying inversely with time, where K is a constant and t is the time in seconds. The integration time T_(i) is determined by dividing one by the frame rate, shown in FIG. 6. One value for K is described below with FIG. 5. Q_(NLi) is one expression for the excess (offset, background, or dark) charge Q_(E) 35 of the measured charge Q_(Ti) 36 for pixel “i” at node 34, and is calculated by integrating the excess current I_(E)(t) over the frame period (integration time). One skilled in the art will recognize that I_(E)(t) modeling is only one method for adjusting for time varying current. In an alternate embodiment, I_(E)(t) may be estimated by using other methods, for example a continuous smooth curve fit. In yet another embodiment, for example, I_(E)(t) is estimated by a theoretical model expression.

FIG. 5 illustrates one example of graph 500 showing current on the vertical axis and time on the horizontal axis, for multiple TFTs connected in parallel. In one embodiment, K may be determined by placing 1000 TFTs in parallel and measuring the current with time varying from 0.0001 to 10 seconds. On graph 500, using a logarithmic scale for the time, the result is estimated as a straight line with a negative slope of ˜T⁻¹. Dividing by the 1000 TFTs results in 10⁻¹⁵ A (amp), which is one value for constant K. One skilled in the art will recognize that other methods of determining a value for K may be used. In one embodiment, for example, K is derived from theoretical values for TFTs. In another embodiment, K may be derived from measuring excess current from a system in which the invention is to be practiced.

Additional ways of modeling the time varying excess current may include: I _(E)(t)=A·t ^(n)  (1)

In equation (1), n may be greater or less than zero but not equal to zero or one. The constant A may either be determined theoretically or by comparison with measured data. Some typical n values are, for examples, −0.3, −0.5, −1.0 and −1.3.

$\begin{matrix} {{I_{E}(t)} = {\sum\limits_{i = {- m}}^{n}{B_{i}{\mathbb{e}}^{D_{i}t}}}} & (2) \end{matrix}$

In equation (2), B_(i) and D_(i) may be constants and on and n may be integers. B_(i), D_(i), m, and n, may be determined either theoretically or by comparison with measured data.

$\begin{matrix} {{I_{E}(t)} = {\sum\limits_{i = {- m}}^{n}{F_{i} \cdot t^{i}}}} & (3) \end{matrix}$

In equation (3), F_(i) may be constant and m and n may be integers. F_(i), m, and n, may be determined either theoretically or by comparison with measured data.

$\begin{matrix} {{I_{E}(t)} = {\sum\limits_{i = {- n}}^{n}{G_{n}{\mathbb{e}}^{{\mathbb{i}}\; n\;\pi\;{T/1}}}}} & (4) \end{matrix}$

In equation (4), G_(n) equals ½T times the integral (from −T_(i) to +T_(i)) of I_(E)(x) e^(−inπx/T) with respect to x, and T_(i) is the integration time interval of interest and n is an integer large enough for the calculated I_(E)(T_(i)) value to approximate the observed value to the desired precision.

FIG. 6 illustrates a table correlating frame rate with integration time. Integration time (T_(i)) is 1 divided by the frame rate. For example, a frame rate of 0.1 frames per second (FPS) yields an integration time of 10 seconds, a frame rate of 1 FPS yields an integration time of 1 second, a frame rate of 30 FPS yields an integration time of 0.033 seconds, and a frame rate of 100 FPS yields an integration time of 0.01 seconds.

FIG. 7 is a flow diagram illustrating one embodiment of a method of estimating the excess signal S_(E) 235 output from A/D converters 19 (representative of Q_(E) 35 in a pixel of a frame captured by the imager sensor array 16), and compensating for the excess signal S_(E) in the pixel of the captured frame. It should be noted that the method described herein may be implemented by the computing device 4 to generate the excess signal S_(E) 235. The integration time is determined based on the frame rate, step 700. As demonstrated with FIG. 6, integration time is the reciprocal of the frame rate. One skilled in the art will recognize that integration time is also used for methods other than integration.

The method determines a value for K as discussed, for example, above in relation to FIG. 5, step 710. In step 720, an estimation of the excess signal S_(E) 235 composed of linear and non-linear background signal S_(NL), and/or non-linear lag signal S_(LAG), based on the constant (K) value and the frame rate, is calculated. In one embodiment, the excess signal S_(E) 35 may be calculated, for example, by integrating I_(E)(t), with the determined value of K, over the integration time (T)(the reciprocal of the frame rate), as described above with respect to FIG. 4. In another embodiment, the excess signal S_(E) 235 may be calculated by summing I_(E)(t) over a series of steps. In step 730, the estimation of excess signal S_(E) 235 is subtracted from a measured signal S_(T) 236. The measured signal S_(T) 236 is, for example, representative of the measured charge Q_(T) 36 read out of a node 34 of FIG. 2B at an appropriate time and contains contributions from the charge stored on capacitor 28, also in FIG. 2B, as well as non-linear charge contributions (excess charge 35) from TFT 32 if the frame rate is below 20 seconds per frame, see FIG. 1. The result from step 730 includes an estimation of the excess signal S_(E) 235 arising from radiation incident on photodiode 26 a from one or more prior frames that constitutes a lag contribution. In an alternative embodiment, the processor 6 may use a look-up table storing excess signal S_(E) 235 estimates versus integrated time values based on frame rates.

FIG. 8 is a flow diagram illustrating one embodiment of a method of estimating the excess signal S_(E) 235 from a pixel of a frame captured by the imager sensor array 16 using one reference image frame, and compensating for the excess signal S_(E) 235 from the pixel of the captured frame. Each pixel of the reference image frame has a measured signal S_(T) 236. The excess signal S_(E) 235 may be estimated using the measured signal S_(T) 236 from each pixel of the reference image frame and the difference in time between the end of exposure of a high-dose radiographic image and the frame time of the corrected image frame. The estimated excess signal S_(E) 235 is then subtracted from the measured signal S_(T) of the corrected image frame to produce the true image signal S_(S) 239.

In one embodiment, the excess signal S_(E) 235 may be estimated using a power function (described below). In another embodiment, the excess signal S_(E) 235 may be estimated using a look-up table (described below). First, the method selects a frame rate, step 800. In step 810, anon-saturated, non-exposed image frame of the measured signal S_(T) 236 is selected as a reference image frame. In step 820, the method determines the difference in time between the frame time of the selected reference image frame and the end of exposure time of the high-dose radiographic image. This difference in time may be determined using the frame rate. In another embodiment, time may be represented as frame numbers. In step 830, the excess signal S_(E) 235 of an image frame is estimated using the measured signal S_(T) 236 of the reference image frame and the difference in time between the end of exposure time and the frame time of the corrected image frame. The method in step 840 subtracts the estimated excess signal S_(E) 235 of an image frame from the measured signal S_(T) 236 of the corrected image frame to produce the true image signal S_(S) 239. It should be noted that this method may be repeated for all pixels of an image frame. The true image signal S_(S) 239 of each pixel of a frame provides a corrected image frame without significant image errors and artifacts that may appear in the image frame as “ghost” images from radiation incidents during one or more prior frames.

FIG. 9 is a flow diagram illustrating one embodiment of a method of estimating the excess signal S_(E) 235 in a pixel of a frame generated by the imager sensor array 16 using two reference image frames, and compensating for the excess signal S_(E) 235 in the pixel of a captured frame. Each pixel of the first and second reference image frames has the corresponding measured signals S_(T) 236. The excess signal S_(E) 235 may be estimated using the measured signal S_(T) 236 of each pixel of the first reference image frame, the measure signal S_(T) 236 of each pixel of the second reference image frame, the difference in time between the first frame time of the first reference image frame and the second frame time of the second reference image frame and the difference in time between the frame time of the first or second reference image frame and the frame time of the captured image frame to be corrected. The estimated excess signal S_(E) 235 is then subtracted from the measured signal S_(T) 236 of the corrected image frame to produce the true image signal S_(S) 239. The sources of excess signal S_(E) 235 may be contributions from, for examples, leakage currents, dark/offset currents, and lag currents from the capacitor 28, and/or from the photoconductor 26, of the imager sensor array 16. It should be noted that the excess charge Q_(E) 35 remaining from a radiographic image may create a “ghost” image in the subsequent fluoroscopic images. Estimating and compensating for the signal S_(E) 235 representative of the excess charge Q_(E) 35, reduces the residual “ghost” images presented by previous frames.

In one embodiment, the excess signal S_(E) 235 may be estimated using a power function (described below). In one embodiment, the excess signal S_(E) 235 may be estimated using a look-up table (described below). First, the method selects a frame rate, step 900. In step 910, two non-saturated, non-exposed image frames are selected as first and second reference image frames. In step 920, the method determines the difference in time between the first frame time of the first reference image frame and the second frame time of the second reference image frame. This difference in time may be determined using the frame rate. In another embodiment, time may be represented as frame numbers. In step 930, the excess signal S_(E) 235 of an image frame is estimated using the at least one of the measured signal S_(T) 236 of the first and second reference image frames and the difference in time between the first and/or second frame times to the selected frame for compensation. The method in step 940 subtracts the estimated excess signal S_(E) 235 of an image frame from the measured signal S_(T) 236 of the image frame to produce the true image signal S_(S) 239. It should be noted that this method may be repeated for all pixels of an image frame. The true image signal S_(S) 239 of each pixel of a frame creates a corrected image frame without significant image errors and artifacts that may appear in the image frame as “ghost images” from radiation incidents during one or more prior frames.

FIGS. 10A and 10B are exemplary fluoroscopic image frames illustrating compensation for excess signal S_(E) 235 in an image F 1000 to produce the true image F 1010. FIGS. 10A and 10B contain the same fluoroscopic frame acquired shortly after radiographic exposure, uncompensated image frame F 1000 and compensated image frame F 1010. For the radiographic exposure, 20 cm of acrylic were placed at an angle on the imager sensor array 16. Approximately 3 seconds after the radiographic exposure the acrylic block was moved such that it became aligned to the horizontal orientation of the imager sensor array 16 and the fluoroscopic acquisition was started. Uncompensated frame F 1000 was acquired approximately 13 seconds after the radiographic exposure. The bright triangle shaped areas 1020 in the upper left hand corner and lower right hand corner in FIG. 10A are due to signal contribution of the radiographic “ghost.” The compensated frame F 1010 of FIG. 10B uses the same window and level as used for FIG. 10A. The triangular shaped areas 1030 of FIG. 10B are significantly less visible than the triangle shaped areas 1020 of FIG. 10A.

FIGS. 11A and 11B are exemplary fluoroscopic image frames illustrating compensation for signal S_(E) 235 in an image G 1100 to produce the true image G 1110 of a pelvis phantom. FIGS. 11A and 11B contain the same fluoroscopic frame acquired shortly after radiographic exposure, uncompensated image frame G 1100 and compensated image frame G 1110. The uncompensated frame G 1100 displayed in FIG. 11A shows an area 1130 where the signal contribution from the radiographic “ghost” introduces a visible image artifact 1140. FIG. 11B illustrates a compensated image frame G 1110 after estimating and compensating for the signal S_(r) 235 in the uncompensated image frame G1100. The compensation of signal S_(E) 235 reduces the artifact 1140 of the area 1130 of FIG. 11A.

FIG. 12 illustrates one example of a graph 1200 showing the measured signal level as a function of time of imaging system 2. The measured signal level in time has two stages. The first stage is the measured signals during the exposure time T_(exp) 1220 of a non-saturated exposed image 1211 of the imaging system 2. The second stage of the measured signal levels shows the non-saturated excess signal 1212 after the end of exposure time T_(exp) 1220. The measured signal S_(T) 236 is obtained A/D conversion of the measured charge at node 34 as previously discussed in relation to FIGS. 2A-2C.

The measured signal S_(T) 236 of the high-dose non-saturated exposed image 1211 of FIG. 12 is represented as being a constant line at a charge level L_(ref) 1251. In another embodiment, the measured high-dose non-saturated exposed image 1211 may be illustrated as a time-varying function. The measured charge of the high-dose non-saturated exposed image 1211 is measured at charge level L_(ref) 1251 below the signal saturation level L_(SAT) 1231. The non saturated excess signal 1212 is the amount of excess signal after the end of exposure time T_(exp) 1220. Sources of the excess signal 1212 may be, for examples, leakage currents, dark/offset currents, and lag contribution currents from the capacitor 28, and/or from the photoconductor 26, and/or from the switch 32, of the imager sensor array 16. If not removed, the contribution due to the excess signal 1212 introduces “ghost” images in the subsequent images.

Graph 1200 illustrates the non-saturated excess signal 1212 having anon-linear decay response after the end of exposure time T_(exp) 1220 of a high dose non-saturated exposed image 1211. An exemplary non-saturated excess signal 1212 automatically begins to decay because the measured high-dose non-saturated exposed image 1211 is at a non-saturated signal level L_(ref) 1251 (L_(ref) 1251 is less than current saturation level L_(SAT) 1231). The method described with respect to FIG. 8 uses the non-saturated excess signal 1212 to estimate the excess signal S_(E) 235 of subsequent frames. As described in FIG. 8, step 810, a non-saturated reference image frame is selected. The reference image frame F_(ref1) 1240 is illustrated in FIG. 12. The method uses the measured non-saturated charge level L_(D1) 1241 and the difference in time t_(D1) 1260, determined in step 820, to estimate the excess signal, step 830. The method subtracts the estimated excess signal S_(E) 235, step 840, to compensate the measured signal S_(T) 236 to produce a true image S_(S) 239 output from imaging system 2. The difference in time t_(D1) 1260 is determined by subtracting the frame time T_(ref1) 1230 of the reference image frame F_(ref1) 1240 of the measured non-saturated excess signal 1212, from the end of exposure time T_(exp) 1220, step 820. In one embodiment, the excess signal S_(E) 235 may be estimated using the difference in time t_(D1) 1260 and the measured L_(D1) 1241 of reference image frame F_(ref1) 1240 in a function of integration time as described previously in relation to FIG. 7. In another embodiment, the excess signal S_(E) 235 may be estimated using the difference in time t_(D1) 1260 and the measured L_(D1) 1241 of reference image frame F_(ref1) 1240 in a power function. In another embodiment, the excess signal S_(E) 235 may be estimated using the difference in time t_(D1) 1260 and the measured L_(D1) 1241 of reference image frame F_(ref1) 1240 in a look-up table. In another embodiment, the excess signal S_(E) 235 may be determined using a power function and a look up table. In another embodiment, the difference in time t_(D1) 1260, the end of exposure time T_(exp) 1220, and the frame time T_(ref1) 1230 of reference image frame F_(ref1) 1240, may be in terms of frame numbers. The frame numbers may be computed using the frame rate as known to one of ordinary skill in the art.

FIG. 13 illustrates one example of a graph 1300 showing the measured signal levels as a function of time of imaging system 2. The measured signal S_(T) 236 in time has three stages. The first stage is the measured signal up to the end of the exposure time T_(exp) 1320 of a high-dose saturated exposed image 1311. The second stage of the measured signal S_(T) 236 shows the saturated excess signal 1312 after the end of exposure T_(exp) 1320. The third stage of the measured signal S_(T) 236 shows the non-saturated excess signal 1313 after the end of saturation time T_(SAT) 1321. The measured signal S_(T) 236 is obtained in the same manner as described in relation to FIG. 12.

The measured signal S_(T) 236 of the high-dose saturated exposed image 1311 of FIG. 13 is represented as being a constant line because the measured signal S_(T) 236 is saturated at the signal saturation level L_(SAT) 1331. The measured saturated excess signal 1312 is also saturated at the signal saturation level L_(SAT) 1331 and is represented as a constant line until the end of saturation time T_(SAT) 1321.

Graph 1300 illustrates the non-saturated excess signal 1313 having a non-linear decay response after the end of exposure time T_(exp) 1320 of a high dose non-saturated exposed image 1311. The method described with respect to FIG. 8 uses the measured non-saturated signal S_(T) to estimate the excess signal S_(E) 235 of subsequent frames. As described in FIG. 8, step 810, a non-saturated reference image frame is selected. The reference image frame signal F_(ref1) 1340 is illustrated in FIG. 13. The method uses the measured non-saturated signal level L_(D1) 1361, the difference in time t_(D1) 1360 and the difference in time between the end of the exposure T_(exp) and the time of the frame being corrected (compensated), as determined in step 820, to estimate the excess signal S_(E) 235, step 830. The method subtracts the estimated excess signal S_(E) 235, step 840, to compensate the measured non-saturated signal 1313 to produce a true image signal S_(S) 239 at the output of imaging system 2. The difference in time t_(D1) 1360 is determined by subtracting the frame time T_(ref1) 1330 of the reference image frame signal F_(ref1) 1340 of the measured non-saturated excess signal 1313, from the end of exposure time T_(exp) 1320, step 820. In one embodiment, the excess signal S_(E) 235 may be estimated using the difference in time t_(D1) 1360 and the measured signal level L_(D1) 1361 of reference image frame signal F_(ref1) 1340 in a function of integration time as described previously in relation to FIG. 7. In another embodiment, the excess signal S_(E) 235 may be estimated using the difference in time t_(D3) 1360 and the measured signal level L_(D1) 1361 of reference image frame signal F_(ref1) 1340 in a power function. In another embodiment, the excess signal S_(E) 235 may be estimated using the difference in time t_(D3) 1360 and the measured signal level L_(D1) 1361 of reference image frame F_(ref1) 1340 in a look-up table. In another embodiment, the excess signal S_(E) 235 may be determined using a power function and a look up table. In another embodiment, the difference in time t_(D3) 1360, the end of exposure time T_(exp) 1320, the end of saturation time T_(SAT) 1321, and the frame time T_(ref1) 1330 of reference image frame F_(ref1) 1340, and the difference in time between the end of exposure time T_(exp) 1320 and the time of the image frame to be corrected, may be in terms of frame numbers. The frame numbers may be computed using the frame rate as known to one of ordinary skill in the art.

FIG. 14 illustrates one example of a graph 1400 showing the measured signal level as a function of time. The measured signal S_(T) 236 in time has three stages. The first stage is the measured signal S_(T) 236 up to the end of the exposure time T_(exp) 1420 of a high-dose saturated exposed image 1410. The second stage of the measured signal S_(T) 236 shows the saturated excess signal S_(E) 1412 after the end of exposure time T_(exp) 1420. The third stage of the measured signal S_(T) 236 shows the non-saturated excess signal S_(E) 1413 after the end of saturation time T_(SAT) 1421. The measured signal S_(T) 236 may be obtained in the same manner as described in relation to FIG. 12. The measured charge of the high-dose saturated exposed image 1410 of FIG. 14 is represented as being a constant line because the signal is saturated at the signal saturation level L_(SAT) 1431. The measured saturated excess signal 1412 is also saturated at signal saturation level L_(SAT) 1431 and is represented as a constant line until the end of saturation time T_(SAT) 1421.

Graph 1400 illustrates the measured non-saturated excess signal 1413 having a non-linear decay response after the end of saturation time T_(SAT) 1421 of a high dose non-saturated exposed image 1411. The method described with respect to FIG. 9 uses the measured non-saturated excess signal 1413 to estimate the excess signal S_(E) 235 of subsequent frames. As described in FIG. 9, step 910, two non-saturated reference image frames are selected. The first reference image frame F_(ref1) 1440 and the second reference image frame F_(ref2) 1441 are illustrated in FIG. 14. The method uses the measured non-saturated signal levels L_(D1) 1481 and L_(D2) 1491, the difference in time t_(D3) 1460 and the difference in time between the first or the second reference frame time and the time of the image frame to be corrected, determined in step 920, to estimate the excess signal S_(E) 235, step 930. The method subtracts the estimated signal S_(E) 235, step 940, to compensate the measured excess signal 1413 to produce a true image charge S_(S) 239. The difference in time t_(D3) 1460 is determined by subtracting the first frame time T_(ref1) 1430 of the reference image frame F_(ref1) 1440 from the second frame time T_(ref2) 1431 of the reference image frame F_(ref2) 1441 of the measured non-saturated excess signal 1413, step 920. In one embodiment, the excess signal S_(E) 235 may be estimated using the difference in time t_(D3) 1460, the measured signal level L_(D1) 1481 and L_(D2) 1491 of reference image frames F_(ref1) 1440 and F_(ref2) 1441 and the difference in time between the first or the second reference frame time and the time of the image frame to be corrected in a function of integration time as described previously in relation to FIG. 7. In another embodiment, the excess signal S_(E) 235 may be estimated using the difference in time t_(D3) 1460, the measure signal level L_(D1) 1481 and L_(D2) 1491 of reference image frames F_(ref1) 1440 and F_(ref2) 1441 and the difference in time between the first or the second reference frame time and the time of the image frame to be corrected in a power function. In another embodiment, the excess signal S_(E) 235 may be estimated using the difference in time t_(D3) 1460, the measure signal level L_(D1) 1481 and L_(D2) 1491 of reference image frames F_(ref1) 1440 and F_(ref2) 1441 and the difference in time between the first or the second reference frame time and the time of the image frame to be corrected in a look-up table. In another embodiment, the excess signal S_(E) 235 may be estimated using the difference in time t_(D3) 1460, the measured signal level L_(D1) 1481 and L_(D2) 1491 of reference image frames F_(ref1) 1440 and F_(ref2) 1441 and the difference in time between the first or the second reference frame time and the time of the image frame to be corrected in a recursive function.

In another embodiment, the difference in time t_(D3) 1460, the end of exposure time T_(exp) 1420, the difference in time t_(D1) 1451, the difference in time t_(D2) 1452, the end of saturation time T_(SAT) 1421 the first frame time T_(ref2) 1430 of the first reference image frame F_(ref1) 1440, the second frame time T_(ref2) 1431 of the second reference image frame F_(ref2) 1441, and the difference in time between the first or second reference frame time and the time of the image frame to be corrected, may be in terms of frame numbers. The frame numbers may be computed using the frame rate as known to one of ordinary skill in the art.

In one embodiment, a power function may be used in estimating the excess signal S_(E) 235, as described in relation to FIGS. 8, 9, 12, 13, and 14. The following description and equations are used as one method of estimating the excess signal S_(E) 235 using a power function. The power function estimates the excess signal S_(E) 235 of the measured signal S_(T) 236. After compensating for the excess signal S_(E) 235 of the measured signal S_(T) 236, using the power function, the excess signal S_(E) 235 may be subtracted from the measured signal S_(T) 236 to produce a corrected true image signal S_(S) 239 without “ghost” images from previous radiographic image frames. It should be noted that the power function estimation of the excess signal S_(E) 235 may be done for each pixel of a frame. The compensation of the excess signal S_(E) 235 may also be done for each pixel of a frame to create true image signal S_(S) 239.

One example of the power function approximation is shown in the following equations.

$\begin{matrix} {{S_{E}(t)} \cong {{S_{E}\left( t_{o} \right)} \cdot t^{- \alpha}}} & (5) \\ {{S_{E}\left( {n\; T} \right)} \cong {{S_{E}\left( t_{o} \right)} \cdot \left( {n\; T} \right)^{- \alpha}}} & (6) \\ {T = \frac{1}{FrameRate}} & (7) \end{matrix}$

Equation (5) approximates the excess signals S_(E) 1212, 1313, and 1413 shown in FIGS. 12, 13, and 14, respectively. S_(E) (t) represents the estimated excess signals 1212, 1313, and 1413. Exponent α can be assumed to be constant for a wide range of radiographic exposures. The continuous time variable t is the time after the end of exposure T_(exp) 1220, 1320, and 1420. S_(E)(t₀) represents a lag reference constant of the excess signals 1212, 1313, or 1413. Constant S_(E)(t₀) is unique for each radiographic exposure. In another embodiment, the continuous time variable t of equation (5) may be replaced with discrete frame time nT, equation (6). T is the reciprocal of the frame rate of the imager sensor array 16, equation (7). The variable n is a positive integer such that discrete frame time nT is greater than end of exposure time T_(exp) 1220, 1320, and 1420. Equation (6) illustrates this substitution and shows the discrete nature of the imager sensor array 16. S _(Ecomp)(t)=S _(Emeas)(t)−S _(E)(t)  (8) S _(Ecomp)(t)=S _(Emeas)(t)−S _(E)(t _(o))·(t)^(−α)  (9)

Equation (8) illustrates how the excess signal S_(E) of image F is subtracted from the measured signal S_(T) 36 of Frame F to obtain the compensated signals S_(S)(t). S_(S)(t) represents the charge of frame F after compensation as a function of time. S_(T)(t) represents the measured charge of frame F before compensation at a particular point in time after T_(exp) 1220, 1320, and 1420. S_(E) (t) represents, as described in relation to (5), the approximation of the excess signals 1212, 1313, and 1413 as a function of time, as shown in FIGS. 12, 13, and 14, respectively. Combining the two equations (5) and (8), results in equation (9). S _(Ecomp)(nT)=S _(Emeas)(nT)−S _(E)(nT)  (10) S _(Ecomp)(nT)=S _(Emeas)(nT)−S _(E)(t _(o))·(nT)^(−α)  (11)

Equation (10) illustrates how the excess signal S_(E) of image F is subtracted from the measured signal S_(T) 26 of Frame F to compensate for that excess signal S_(E) 235 as a function of frame number. S_(s)(nT) represents the charge of frame F after compensation as a function of frame number. S_(T)(nT) represents the measured signal S_(T) 236 of frame F before compensation for a particular frame. S_(E)(nT) represents, as described in relation to equation (6), the approximation of the excess signals 1212, 1313, and 1413 as a function of frame number. Combining the equations (6) and (10) results in equation (11). S _(E)(t _(o))(t _(D1))=L _(D1) ·t _(D1) ^(α)  (12) t _(D1) =T _(ref1) −T _(exp)  (13) S _(E)(t)=S _(E)(t)−(L _(D1) ·t _(D1) ^(α))·(t)^(−α)  (14)

Equation (12) illustrates how the lag reference constant S_(E)(t₀) is derived if the time reference t_(D1) is known. Time reference t_(D1) represents the difference in time of the end of the exposure T_(exp) and the time of reference of the first reference image frame acquired T_(ref1), as shown in equation (13). Examples of t_(D1) are shown in FIGS. 12, and 13, as the difference in time t_(D1) 1260, and the difference in time t_(D1) 1360, respectively. Signal level L_(D1) 1241 and signal level L_(D1) 1361 of FIGS. 12, and 13, represent the measured signal of the acquired reference image frames F_(ref1) 1240, and F_(ref1) 1340, respectively. Combining equations (9) and (12) results in equation (14). It should be noted that the variable t of equations (12), (13), and (14) may be in terms of a particular frame number in discrete frame time nT. The particular frame number in discrete frame time nT, is determined by n, the positive integer frame number, and the reciprocal of the frame rate, T (see equation (7)).

$\begin{matrix} {t_{D\; 1} \approx \frac{t_{D\; 3}}{\left( {\left( \frac{L_{D\; 1}}{L_{D\; 2}} \right)^{\frac{1}{\alpha}} - 1} \right)}} & (15) \\ {t_{D\; 3} = {t_{{ref}\; 2} - t_{{ref}\; 1}}} & (16) \\ {L_{D{({k + 1})}} = {L_{D\; 1} \cdot \left( {1 + {k \cdot \left( {\left( \frac{L_{D\; 1}}{L_{D\; 2}} \right)^{\frac{1}{\alpha}} - 1} \right)}} \right)^{- \alpha}}} & (17) \\ {L_{D{({k + 1})}} = {L_{D\; 1} \cdot \left( \frac{1}{\left( {1 + {k \cdot \left( \frac{L_{D\; 1}}{L_{D\; 2}} \right)} - 1} \right)} \right)}} & (18) \end{matrix}$

Equation (15) illustrates how to approximate the time t_(D1) used in equation (12) to calculate the lag reference constant S_(E)(t₀), if the time elapsed between the end of the radiographic exposure T_(exp) 1420 and the time references T_(ref1) 1430 and T_(ref2) 1431 of FIG. 14 are unknown. The difference in time t_(D3) 1460 is the difference in time between the first frame time T_(ref1) 1430 of the first reference image frame 1440 and the second frame time T_(ref2) 1431 of the second reference image frame 1441, equation (15). Signal level L_(D1) represents the measured charge of the first reference image frame F_(ref1) 1440. Signal level L_(D2) represents the measured charge of the second reference image frame F_(ref2) 1490. If difference in time t_(D3) 1460 is set equal to time T of equation (15), which is the reciprocal of the frame rate (equation (7)), then equations (12) and (14) may be combined to become equation (17). The variable k of equation (17) represents a positive integer number starting at one. Signal level L_(D(k+1)) of equation (17) represents the estimated excess signal S_(E) 235 for the next frame. Measured values for the constant α of equation (17) range from 1.05 to 1.08 in imager sensor array 16. In one embodiment, in order to simplify hardware implementation the constant α may be set to equal 1.0. The simplified equation (17), substituting the constant α with the number 1.0, is shown in equation (18).

FIG. 15 illustrates one example of a look-up table used to index the pre-calculated estimated excess signals using the measured signals at a given time. The selected excess signal may then be compensated for in the measured signals to produce the true signal of the image. The look-up table is used in one embodiment, to index a pre-calculated excess signal to estimate the excess signal S_(E) as a function of time. In another embodiment, the look-up table is used to index a pre-calculated excess signal to estimate the excess signal S_(E) as a function of frame number. The frame number and the measured charges of the reference image frame are used to index the corresponding pre-calculated excess charge. The indexed pre-calculated excess signal may be subtracted from the measured signal of the image to produce the true image signal S_(S). It should be noted that pre-calculated excess signal may be indexed for each pixel. The true image signal S_(S) of each pixel creates a true image frame signal.

In one embodiment, the look up table 1500 may use frame numbers 1510 and the measured reference image frame signals 1520 to index pre-calculated excess signals S_(PRE) 1530. The frame numbers 1510 may correspond to the frame times T_(ref1) 1230, T_(ref1) 1330, T_(ref1) 1430, and T_(ref1) 1431 of FIGS. 12, 13, and 14. The measured reference image frame signals 1520 may correspond to the measured signal levels L_(D1) 1241, L_(D1) 1361, L_(D1) 1481, and L_(D2) 1491 of the selected reference image frames 1240, 1340, 1440, and 1441, respectively. Pre-calculated excess signals S_(PRE) 1530, in one embodiment, may be pre-calculated estimations of the excess signal S_(E) 235 using the integration function of FIG. 4. In another embodiment, the pre-calculated excess signals S_(PRE) 1530 may be pre-calculated using the power function. In another embodiment, the pre-calculated excess signals S_(PRE) 1530 may be pre-calculated by testing the behavior of the sensor array through a non-linear range of operation. In another embodiment, the pre-calculated excess signals S_(PRE) 1530 may be determined by simulating the behavior of a sensor array through a non-linear range of operation. In another embodiment, the pre-calculated excess signals S_(PRE) 1530 may be determined by theorizing the behavior of sensor array through a non-linear range of operation. The pre-calculated excess signals S_(PRE) 1530 may then be subtracted from the measured signal S_(T) 236 of an image frame to compensate for the excess signal S_(E) 235 present in the measured signal S_(T) 236.

In another embodiment, a recursive function may be used in estimating the excess signal S_(E) 235. The following description and equations are used as one method of estimating the excess signal S_(E) 235 using a recursive function. The recursive function estimates the excess signal S_(E) 235 of a frame (N) to be corrected using the calculated excess signal S_(E) 235 of the previous frame (N−1) and a coefficient α, which is recalculated for every consecutive frame to be corrected. The coefficient α for the first frame to be corrected is determined using the measured signal S_(T) 236 of the two previous consecutive reference frames. After estimating the excess signal S_(E) 235 using the recursive function, the excess signal S_(E) 235 may be subtracted from the measured signal S_(T) 236 of the frame to produce a corrected true image signal without any “ghost” images that may be introduced by previous radiographic image frames. S _(EN) =S _(EN-1)·α_(N)  (19) α_(N)=α_(N-1) +Kp·(1−α_(N-1))²  (20)

One example of the recursive function approximation is shown in equations (19) and (20). The recursive function in equation (19) calculates the excess signal S_(EN) of the lag frame N by multiplying the excess signal S_(EN-1) of the previous lag frame N−1 by a coefficient α_(N). Coefficient α_(N) is calculated in equation (20) using a constant Kp and the coefficient of the previous frame α_(N-1). Constant Kp is dependent on the attributes of the imager sensor array 16 and, in one embodiment, may be in the range of 0.5 to 1.1. Coefficient α_(N) is calculated for every new frame.

FIG. 16A illustrates one example of a graph showing the remaining excess signal S_(E) 235 of an image after compensation using three different estimation functions as a function of frame number. The error signal count 1610 resulting from the estimation methods 1640, 1650, and 1660, illustrated in FIGS. 16A and 16B, are examples of the estimations made in the steps 720, 830, and 930 of the methods described in FIGS. 7, 8, and 9, respectively. The graph 1600 a includes the error signal count 1610 of the actual measured signal S_(T) 236 of an image 1630 without compensation for the excess signal S_(E) 235. The graph 1600 a also includes the error signal count 1610 of the remaining excess signal S_(E) 235 after compensation using three different estimation methods as a function of frame number 1620. The three estimation methods are a constant decay function 1640, a power function 1650, and a recursive function 1660.

FIG. 16B illustrates the same remaining excess signal S_(E) 235 for two of the estimation methods as a function of frame number at a smaller scale than FIG. 16A. Graph 1600 b illustrates the error signal counts 1610 of the power function 1650, and the recursive function 1660. The actual excess signal S_(E) without compensation 1630, and the constant decay function 1640 are not shown in graph 1600 b because they are outside the scale of the graph. In mixed radiographic/fluoroscopy applications, lower dose fluoroscopy images are acquired shortly after a higher dose radiographic exposure. The remaining excess signal from the radiographic exposure may appear as a “ghost” image in the fluoroscopic images. If the error count of the remaining excess signal S_(E) 235 after compensation can be lowered the “ghost” appearing in the images can be corrected. The error counts illustrated in FIG. 16B correspond to an x-ray dose of approx. 0.5 uR/frame, which is about half of the minimum dose recommended for the fluoroscopy mode of imager sensor array 16. An estimation of excess signal method that permits the error signal count 1610 to be below 400 error counts after compensation may reduce or correct any “ghost” images that may be present in subsequent fluoroscopic images that are introduced from previous radiographic exposures. Compensation using the estimation method of constant decay 1640 of FIG. 16A may not sufficiently compensate for the excess signal because the levels of the error signal count 1610 have a maximum absolute magnitude above 400-error count. The remaining excess signal after compensation using the power function 1650 and the recursive function 1660 have maximum absolute magnitudes lower than 10 counts. The power function 1650 and the recursive function 1660 having an error signal count lower than 10 may sufficiently reduce or correct any “ghost” images that may be present due to excess signal S_(E) 235.

The particular methods of the invention have been described in terms of computer software with reference to a series of flowcharts. The methods to be performed by computing device 4 constitute computer programs made up of computer-executable instructions illustrated as blocks (acts). Describing the methods by reference to a flowchart enables one skilled in the art to develop such programs including such instructions to carry out the methods on suitably configured computers (the processing unit of the computer executing the instructions from computer-readable media). The computer-executable instructions may be written in a computer programming language or may be embodied in programmable or discrete logic. If written in a programming language conforming to a recognized standard, such instructions can be executed on a variety of hardware platforms and for interface to a variety of operating systems. In addition, the present invention is not described with reference to any particular programming language. It will be appreciated that a variety of programming languages may be used to implement the teachings of the invention as described herein. Furthermore, it is common in the art to speak of software, in one form or another (e.g., program, procedure, process, application, module, logic . . . ), as taking an action or causing a result. Such expressions are merely a shorthand way of saying that execution of the software by a computer causes the processor of the computer to perform an action or a produce a result. It will be appreciated that more or fewer processes may be incorporated into the methods as described above without departing from the scope of the invention, and that no particular order is implied by the arrangement of blocks shown and described herein.

In the foregoing specification, the invention is described with reference to specific embodiments thereof. It will, however, be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the invention as set forth in the appended claims. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense. 

What is claimed is:
 1. An apparatus, comprising: an imager; and a processor coupled with the imager and configured to: estimate an excess signal based on a non-linear correction to a decay response model and a frame rate; and compensate for the excess signal in the image frame of an imaging system; wherein the frame rate is faster than one tenth of a frame per second.
 2. The apparatus of claim 1, wherein the correction to the decay response model comprises a non-linear time variant decay response model.
 3. The apparatus of claim 1, wherein the correction to the decay response model comprises a representation of a measured signal of the image frame, and wherein the frame rate comprises a frame rate of a measured signal of an image frame.
 4. The apparatus of claim 1, further comprising the processor configured to select the frame rate.
 5. The apparatus of claim 1, wherein the frame rate is faster than 10 frames per second.
 6. The apparatus of claim 1, wherein the non-linear correction comprises a model based on one of a frame rate, a time difference between a frame time of a reference image and of exposure, an integral for a function over time, indexing a lookup table, integration of a smooth curve fit of experimentally derived excess signal data as a function of time, or any combination thereof.
 7. An apparatus, comprising: an imager; and a processor coupled with the imager and configured to: estimate an excess signal based on a non-linear correction to a decay response model of a non-saturated frame of a measured signal of an image frame of an imaging system; and compensate for the excess signal in the image frame using the estimated excess signal.
 8. The apparatus of claim 7, wherein correction to the decay response model comprises a non-linear time variant decay response model.
 9. The apparatus of claim 7, wherein the correction to the decay response model comprises a representation of a measured signal of the image frame.
 10. An apparatus, comprising: an imager; and a processor coupled with the imager and configured to: estimate an excess signal based on a non-linear time variant correction to a decay response model of a measured signal of an image frame of an imaging system; and subtract the excess signal from the measured signal of the image frame.
 11. An apparatus, comprising: an imager; and a processor coupled with the imager and configured to: estimate an excess signal based on a non-linear correction to a decay response model of a measured signal of an image frame of an imaging system; and compensate for the excess signal in the image frame, wherein estimating the excess signal further comprises selecting a first reference image frame and selecting a second reference image frame.
 12. The apparatus of claim 11, wherein estimating is further based on a difference between two lag frames.
 13. The apparatus of claim 11, wherein the correction to the decay response model comprises a non-linear time variant decay response model.
 14. The apparatus of claim 11, wherein the correction to the decay response model comprises a representation of a measured signal of the image frame.
 15. A system, comprising: an x-ray source; an imager to receive x-rays generated by the source; and a processor coupled with the imager and configured to: estimate an excess signal based on a non-linear correction to a decay response model and a frame rate; and compensate for the excess signal in the image frame of an imaging system; wherein the frame rate is faster than one tenth of a frame per second.
 16. The system of claim 15, wherein the correction to the decay response model comprises a non-linear time variant decay response model.
 17. The system of claim 15, wherein the correction to the decay response model comprises a representation of a measured signal of the image frame, and wherein the frame rate comprises a frame rate of a measured signal of an image frame.
 18. The systems of claim 15, further comprising the processor configured to select the frame rate.
 19. The system of claim 15, wherein the frame rate is faster than 10 frames per second.
 20. The system of claim 15, wherein non-linear correction comprises a model based on one of a frame rate, a time difference between a frame time of a reference image and of exposure, an integral for a function over time, indexing a lookup table, integration of a smooth curve fit of experimentally derived excess signal data as a function of time, or any combination thereof.
 21. A system, comprising: an x-ray source; an imager to receive x-rays generated by the source; and a processor coupled with the imager and configured to: estimate an excess signal based on a non-linear time variant correction to a decay response model of a measured signal of an image frame of an imaging system; and subtract the excess signal from the measured signal of the image frame.
 22. The system of claim 21, wherein the correction to the decay response model comprises a representation of a measured signal of the image frame, and wherein the correction to a model comprises a frame rate of a measured signal of an image frame.
 23. The system of claim 21, further comprising the processor configured to select the frame rate.
 24. The system of claim 21, wherein the non-linear time variant correction comprises a model based on one of a frame rate, a time difference between a frame time of a reference image and of exposure, an integral for a function over time, indexing a lookup table, integration of a smooth curve fit of experimentally derived excess signal data as a function of time, or any combination thereof. 